Re: Computable functions/reals.

On Mon, 18 Aug 2008 17:20:59 -0700 (PDT), reasterly@xxxxxxxxx wrote:

On Aug 18, 1:39 pm, "David C. Ullrich" <dullr...@xxxxxxxxxxx> wrote:
In article
<c3fff4e7-3a23-4836-be14-4ba0d872e...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

How do you know what is on the output tape
if the TM doesn't halt?

You don't ever see _all_ of the output.

You are proposing a model of computation
where no calculation can ever be completed?
I'm glad computers don't rely on such a model.

Computers don't do calculations with real numbers.

I don't see how any model of computation can do
calculations with real numbers.

We can prove any machine that reads one
character at a time from a tape can only
read a finite number of characters.

Any machine that writes one character at
a time can only produce finite strings.

Your function f(x) = 2x doesn't work, either,
even if we assume the input is a Cauchy
set of rationals. For example, say I give
you this sequence:

(9/10, 99/100, 999/1000, ...)

Your function returns:

{18/10, 198/100, 1998/1000, ...)

This hardly looks like a Cauchy sequence
for 2.000... to me.

What?????????????????????????????????????

Russell
- Reals numbers aren't really

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

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